The role of visualisation in redefining the pedagogy of fractions in mathematics classrooms among senior primary school teachers
- Authors: Ausiku, Charity Makwiliro
- Date: 2022-10-14
- Subjects: Mathematics Study and teaching (Elementary) Namibia , Fractions Study and teaching (Elementary) Namibia , Visualization , Visual learning , Dual-coding hypothesis , Constructivism (Education) Namibia
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/405456 , vital:70173 , DOI 10.21504/10962/405456
- Description: This mixed methods study explored the impact of the use of a visualisation approach on the pedagogy of eight teacher participants who were involved in the Rundu Campus Fraction Project (RCFP). The aim of this study was to determine the extent to which participants incorporated visualisation processes in the pedagogy of fractions, in view of their exposure to visualisation activities in the RCFP. Since fractions are difficult to teach and learn, visualisation was considered as an alternative approach to the pedagogy of fractions because it presents learners with opportunities to improve their proportional and spatial reasoning. This study was founded on the premise that the incorporation of both verbal and nonverbal cues can enhance the teaching and learning of fractions rather than the use of a single cue. Hence, the two theories underpinning this study are the Dual Coding Theory and the Constructivist Theory. While the Dual Coding Theory advocates for the use of verbal and nonverbal codes, the Constructivist theory states that meaningful learning occurs when learners are presented with opportunities to construct their own knowledge. Thus, the two codes are intertwined. In other words, the active construction of knowledge among learners is aided by using constructivist teaching approaches through the incorporation of both verbal and nonverbal codes. Although this study was predominantly qualitative, quantitative methods were also used in the data collection process. A questionnaire was administered to identify teacher participants for this study, based on their teaching orientations. Their views on best practices in mathematics classrooms in general and the incorporation of visualisation processes in particular, were instrumental in the selection of participants for this study. In addition, observations and semi-structured interviews were also used as research methods. Twenty-five lesson samples were video recorded, transcribed and analysed using both qualitative and quantitative methods. Moreover, each of the eight participants was exposed to a set of pre- and post-observation interviews during which they were expected to express their views on the selection, incorporation and impact of visualisation processes on the teaching of fractions. Data sets from all three instruments were analysed using both quantitative and qualitative methods. The findings indicate that the RCFP had an impact on the teaching strategies employed by the participants as they all incorporated visualisation processes into their teaching to some extent. In some lessons, the visual code was effectively blended into the verbal code while in others, the purpose of and connection between the two codes was not evident. Hence, although all the participants embraced the incorporation of visualisation in the pedagogy of mathematics, some of them struggled to find its rightful position in the teaching of fractions. The findings suggest that despite the participants’ eagerness to use visualisation in their fraction lessons, some of them did not have adequate knowledge to successfully merge it with the conventional verbal code. Thus, for the integration of visuals to be impactful, it should be carefully merged in the teaching of fractions by taking into account various factors. , Thesis (PhD) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-10-14
- Authors: Ausiku, Charity Makwiliro
- Date: 2022-10-14
- Subjects: Mathematics Study and teaching (Elementary) Namibia , Fractions Study and teaching (Elementary) Namibia , Visualization , Visual learning , Dual-coding hypothesis , Constructivism (Education) Namibia
- Language: English
- Type: Academic theses , Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/405456 , vital:70173 , DOI 10.21504/10962/405456
- Description: This mixed methods study explored the impact of the use of a visualisation approach on the pedagogy of eight teacher participants who were involved in the Rundu Campus Fraction Project (RCFP). The aim of this study was to determine the extent to which participants incorporated visualisation processes in the pedagogy of fractions, in view of their exposure to visualisation activities in the RCFP. Since fractions are difficult to teach and learn, visualisation was considered as an alternative approach to the pedagogy of fractions because it presents learners with opportunities to improve their proportional and spatial reasoning. This study was founded on the premise that the incorporation of both verbal and nonverbal cues can enhance the teaching and learning of fractions rather than the use of a single cue. Hence, the two theories underpinning this study are the Dual Coding Theory and the Constructivist Theory. While the Dual Coding Theory advocates for the use of verbal and nonverbal codes, the Constructivist theory states that meaningful learning occurs when learners are presented with opportunities to construct their own knowledge. Thus, the two codes are intertwined. In other words, the active construction of knowledge among learners is aided by using constructivist teaching approaches through the incorporation of both verbal and nonverbal codes. Although this study was predominantly qualitative, quantitative methods were also used in the data collection process. A questionnaire was administered to identify teacher participants for this study, based on their teaching orientations. Their views on best practices in mathematics classrooms in general and the incorporation of visualisation processes in particular, were instrumental in the selection of participants for this study. In addition, observations and semi-structured interviews were also used as research methods. Twenty-five lesson samples were video recorded, transcribed and analysed using both qualitative and quantitative methods. Moreover, each of the eight participants was exposed to a set of pre- and post-observation interviews during which they were expected to express their views on the selection, incorporation and impact of visualisation processes on the teaching of fractions. Data sets from all three instruments were analysed using both quantitative and qualitative methods. The findings indicate that the RCFP had an impact on the teaching strategies employed by the participants as they all incorporated visualisation processes into their teaching to some extent. In some lessons, the visual code was effectively blended into the verbal code while in others, the purpose of and connection between the two codes was not evident. Hence, although all the participants embraced the incorporation of visualisation in the pedagogy of mathematics, some of them struggled to find its rightful position in the teaching of fractions. The findings suggest that despite the participants’ eagerness to use visualisation in their fraction lessons, some of them did not have adequate knowledge to successfully merge it with the conventional verbal code. Thus, for the integration of visuals to be impactful, it should be carefully merged in the teaching of fractions by taking into account various factors. , Thesis (PhD) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-10-14
An analysis of selected Grade 8 mathematics teachers’ use of gestures as visualisation tools to support mathematical meaning-making
- Authors: Haipinge, David Tuhafeni
- Date: 2021-10-29
- Subjects: Gesture , Gesture in mathematics education , Visual learning , Visualization , Mathematics Study and teaching (Secondary) Namibia
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191969 , vital:45184
- Description: The purpose of this Namibian case study was to investigate how different types of gestures are used to support the construction of mathematical meaning making in teaching and learning. Gestures of three selected Grade 8 mathematics teachers were observed and analysed. This study was intended to answer the following research question: how do selected Grade 8 mathematics teachers use gestures as visualisation tools to support mathematical meaning making? The study was framed by an enactivist perspective and the research was oriented in the interpretive paradigm. Data were collected through video-recorded observations of three selected teachers and through stimulus recall interviews. In order to generate rich data and support validity, five lessons per selected teacher were video recorded. The study found that the participating teachers incorporated a variety of mathematical gestures into their lessons in order to support and provide mathematical meaning. Further, this study found that gestures facilitated meaning making in mathematics. The findings in the study suggest a need for mathematics teachers to be trained in using gestures appropriately to communicate mathematically in their lessons. In addition, this study discovered a new type of gesture – the overlapping gesture in addition to McNeill's (1992) types, namely: pointing gestures, metaphor gestures, beating gestures and iconic gestures. This case study also showed that the more experienced the teachers are, the more mathematical gestures they produce during their mathematics lessons. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: Haipinge, David Tuhafeni
- Date: 2021-10-29
- Subjects: Gesture , Gesture in mathematics education , Visual learning , Visualization , Mathematics Study and teaching (Secondary) Namibia
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/191969 , vital:45184
- Description: The purpose of this Namibian case study was to investigate how different types of gestures are used to support the construction of mathematical meaning making in teaching and learning. Gestures of three selected Grade 8 mathematics teachers were observed and analysed. This study was intended to answer the following research question: how do selected Grade 8 mathematics teachers use gestures as visualisation tools to support mathematical meaning making? The study was framed by an enactivist perspective and the research was oriented in the interpretive paradigm. Data were collected through video-recorded observations of three selected teachers and through stimulus recall interviews. In order to generate rich data and support validity, five lessons per selected teacher were video recorded. The study found that the participating teachers incorporated a variety of mathematical gestures into their lessons in order to support and provide mathematical meaning. Further, this study found that gestures facilitated meaning making in mathematics. The findings in the study suggest a need for mathematics teachers to be trained in using gestures appropriately to communicate mathematically in their lessons. In addition, this study discovered a new type of gesture – the overlapping gesture in addition to McNeill's (1992) types, namely: pointing gestures, metaphor gestures, beating gestures and iconic gestures. This case study also showed that the more experienced the teachers are, the more mathematical gestures they produce during their mathematics lessons. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
Exploring visual probability teaching strategies for enhancing mathematical thinking in grade 11 classrooms
- Nghidinwa, Lavinia Tangi-Jehova
- Authors: Nghidinwa, Lavinia Tangi-Jehova
- Date: 2021-10-29
- Subjects: Mathematics Study and teaching (Secondary) Namibia , Probabilities , Visualization , Learning models (Stochastic processes) , VIPROMaths project
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/192002 , vital:45187
- Description: This Namibian case study aimed to explore the use of visualisation tools associated with different teaching strategies in the teaching of probability concepts in Grade 11 by selected teachers, to promote mathematical thinking. This research project is an integral component of the VIPROMaths project whose goal is to research the effective use of visualisation strategies in the mathematics classroom in the Southern African region. As a mathematics teacher, I have observed that mathematics teaching practices in our classrooms have relatively little connection with actual mathematics and as a result, teaching misses opportunities to promote mathematical thinking. This qualitative case study is underpinned by an interpretive paradigm and it is informed by the dual coding theory. Data was collected through survey questionnaires, reflective journals, field notes, observation schedules and stimulus-recall interviews. Firstly, I piloted my study by conducting a survey with the Grade 10-12 mathematics teachers in the Khomas region. The aim of this survey was to understand and explore how teachers in the Khomas region taught probability prior to the intervention programme. The data was analysed quantitatively using descriptive statistics such as tables and bar graphs. The findings from the survey necessitated the need for an intervention programme with some teachers in the region, focused on the use of visual tools to promote mathematical thinking. Lastly, three schools were selected from which three Grade 11 mathematics teachers were chosen to take part in an intervention programme. The goal was to observe how these three teachers use visual probability teaching strategies to enhance mathematical thinking after participating in an intervention programme. Lesson observations showed that all observed teachers used visual models to generate images and used models to develop a probability idea as well as to create platforms for classroom discussions. Interviews revealed that teachers’ views towards probability have shifted from that of being the centre of knowledge to that of a facilitator. As a result, teachers used different models to build on learners’ prior knowledge, to assess whether they grasped the probability concept and extend their teaching to real-life situations. This study concluded that the teachers need to consider using mathematical models for creating a platform for discussion to ensure that their verbal explanations are in line with the visuals incorporated. Coupled with that, the teachers’ correct use of visual probability teaching strategies has the potential of enhancing learners’ mathematical thinking. Therefore, teachers need to teach the learners how to create visuals for enhancing maximise understanding of probability concepts in mathematics. Furthermore, it is hoped that the findings will be useful to mathematics teachers, scholars and educators to improve the teaching of probability. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: Nghidinwa, Lavinia Tangi-Jehova
- Date: 2021-10-29
- Subjects: Mathematics Study and teaching (Secondary) Namibia , Probabilities , Visualization , Learning models (Stochastic processes) , VIPROMaths project
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/192002 , vital:45187
- Description: This Namibian case study aimed to explore the use of visualisation tools associated with different teaching strategies in the teaching of probability concepts in Grade 11 by selected teachers, to promote mathematical thinking. This research project is an integral component of the VIPROMaths project whose goal is to research the effective use of visualisation strategies in the mathematics classroom in the Southern African region. As a mathematics teacher, I have observed that mathematics teaching practices in our classrooms have relatively little connection with actual mathematics and as a result, teaching misses opportunities to promote mathematical thinking. This qualitative case study is underpinned by an interpretive paradigm and it is informed by the dual coding theory. Data was collected through survey questionnaires, reflective journals, field notes, observation schedules and stimulus-recall interviews. Firstly, I piloted my study by conducting a survey with the Grade 10-12 mathematics teachers in the Khomas region. The aim of this survey was to understand and explore how teachers in the Khomas region taught probability prior to the intervention programme. The data was analysed quantitatively using descriptive statistics such as tables and bar graphs. The findings from the survey necessitated the need for an intervention programme with some teachers in the region, focused on the use of visual tools to promote mathematical thinking. Lastly, three schools were selected from which three Grade 11 mathematics teachers were chosen to take part in an intervention programme. The goal was to observe how these three teachers use visual probability teaching strategies to enhance mathematical thinking after participating in an intervention programme. Lesson observations showed that all observed teachers used visual models to generate images and used models to develop a probability idea as well as to create platforms for classroom discussions. Interviews revealed that teachers’ views towards probability have shifted from that of being the centre of knowledge to that of a facilitator. As a result, teachers used different models to build on learners’ prior knowledge, to assess whether they grasped the probability concept and extend their teaching to real-life situations. This study concluded that the teachers need to consider using mathematical models for creating a platform for discussion to ensure that their verbal explanations are in line with the visuals incorporated. Coupled with that, the teachers’ correct use of visual probability teaching strategies has the potential of enhancing learners’ mathematical thinking. Therefore, teachers need to teach the learners how to create visuals for enhancing maximise understanding of probability concepts in mathematics. Furthermore, it is hoped that the findings will be useful to mathematics teachers, scholars and educators to improve the teaching of probability. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
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